Recently, I had the privilege to present at the amazing California Mathematics Council South (CMC-South) Conference in Palm Springs.  It was my first time presenting at a math conference and it was one of the most enjoyable yet terrifying experiences in my teaching career.

For months leading up to the conference, I received invaluable advice from colleagues, family and friends that helped me prepare for my session that I don’t want to forget. Now that I have had an opportunity to present and time to reflect on everything, I feel that their words of wisdom have a brand new meaning now.

There are two reasons for me writing this post:

(1.) To remind myself what to keep in mind next time I present at a math conference based on the advice I received and from my experience.

(2.) To express gratitude to those of you who attended my session and those of you who helped me along the way.

I decided to write two different letters (one to my future self and the other to my colleagues, friends and family) because I feel it’s the most appropriate space for me to be completely honest and vulnerable.

Here it goes…

A Letter to My Future Self

Dear Daniel,

If you are reading this, you’re probably getting ready for your next presentation at a math conference or are considering writing a proposal for a conference session. If there’s one big idea you should remember, it is this…

Would your session alone be worth the price of the conference registration?

Many people go to conferences to learn more, walk away with new ideas / resources, and, what I believe to be the most important — to be inspired. You need to strive to make sure your session accomplishes this.

Conference registrations are an investment, sometimes both a personal and expensive one, so you better be damn sure that your session is worth their while. You need to put in the time to prepare, organize, and rehearse because those at your session deserve it. They will appreciate it.

Also, don’t forget that the people who show up to your session will be there mainly because of the description of your session. They are choosing to spend their time with you. But, that means that you need to deliver what you say you were going to do. So, make sure that you give those in your session time to experience your activities as a learner, discuss / collaborate with others in the session, and provide them with resources they can use immediately when they return to their classroom.

You want people to leave your session thinking, “That was just what I needed.” If you can do that, then you’ve done your job.

But, whatever you do, make sure you are passionate about whatever it is that you present. It will be very apparent that you believe it what you are saying and that’s contagious.

Share your passion! You got this!



P.S. Make sure to silence your phone during your presentation! You looked like a newb at CMC-S!

A Letter To My Colleagues, Friends and Family

Dear Colleagues, Friends and Family,

For those who attended my session, thank you for spending 90 minutes of your conference with me. CMC-S continues to have incredible sessions and I was honored and beyond flattered that you chose to spend your time with me. I remember feeling speechless minutes before the session began. I hope my session was just what you needed.

For those of you who I am honored to call my friends, thank you for your sound advice and support. Thank you for encouraging me to present and share a passion of mine. Thank you for taking time to meet, e-mail, send numerous text messages and answer phone calls. Thank you for helping me make sense of my ideas, keeping me focused and pushing me to think of ways to make my session better. Each of you have single-handedly made me a better educator and I cannot thank you enough.

For my family, thank you for being some of my biggest cheerleaders. Your love and support does not go unnoticed.

And most importantly, for my wife. Thank you for being absolutely amazing. I would not be the person I am today without you by my side. Thank you for being my biggest inspiration and role model. Thank you for the countless hours helping me prepare for my session. Thank you for helping me cut and fold the cards for the clothesline activities. Thank you for letting me rehearse in front of you. You are the best person I know. I love you so much!

You guys rock!



On a side note, if you attended my session and have a moment, do you mind taking a few minutes to complete the #ObserveMe feedback form, I would great appreciate it. You will help me become better!


For those about to rock, we salute you! \m/ \m/


I came very close to going into shock at the beginning of the school year. Let me elaborate…I promise it has a good ending.

I had the opportunity to work with 6th grade students and I used one of Robert Kaplinsky’s lessons that provides context for least common multiple, which just so happened to come from one of my favorite movies, “Father of the Bride.” (I know, I know…took me long enough to blog about this, right?) To provide some background to the story, this was my first time working with this teacher at this school year. I did not know the students and the teacher had not introduced LCM to her students. I showed her the lesson and she asked if I could do the lesson with her students. Here’s my experience…

How Many Hot Dogs and Buns Should He Buy?

I ran this lesson in three class periods and I would like to think that it finally got better by the third class…#storyofmylife… This was my first time using one of Robert’s lessons and I tried to orchestrate the activity similar to how I’ve seen him do it and based on the suggestions he listed in the lesson.

First attempt:

I began the lesson by providing some background to the movie. I explained that George Banks (Steve Martin) is at the grocery store buying food for dinner. At this point in the movie, George is stressed out about how much his daughter’s wedding is going to cost. If you’ve seen this movie, we come to learn that George Banks is…um…to say it politely…he is very…um…frugal or careful with his money.

After giving the students some information about the movie, I played the clip and asked the students, “What questions do you have?” Hands went up and I was pumped. Here were some of the questions I got:

  • “Why is he wearing a suit?”
  • “Why is he so angry?”
  • “Who is that?”

Hmm…not the questions I thought kids would ask, so I tried another question: “What do you think we are trying to figure out?” The response…crickets. Damn.

Third question — “Why is George so upset?” “Because there is a different number of hot dogs and hot dog buns in each package.” Sweet! I’m not as bad of a teacher as I thought…

“Interesting. What would happen if he buys only one package of hot dogs and one package of hot dog buns?” “He would have 4 extra hot dog buns?” Yes. My batting average is now .500!

How would that make someone feel?” “Angry.” “Mad.” “Upset.” I’m Leonardo diCaprio right now…King of the World!

Okay. Let’s try to help George not be so upset. Let’s investigate this question…‘How many packages of hot dogs and packages of hot dog buns should he buy?’”

I used Robert’s Problem Solving Framework and asked the students to write the question on their worksheet and make a guess. Then, I asked the students to list everything they absolutely knew about the problem and what we need to know to solve the problem. To raise their level of concern, I stole a strategy from Robert and told the students, “I won’t provide you information about the problem unless you ask for it.” Here’s what the class came up with:

What do you already know from the problem? What do you need to know to solve the problem?
  • There are 8 hot dogs in one package
  • There are 12 hot dog buns in one package
  • He’s cheap
  • His daughter is getting married
  • How many people are eating dinner?
  • How much money does he have?
  • How much does one package of hot dogs cost?
  • How much does one package of hot dog buns cost?

After we confirmed the information that we already knew, I went through each of the questions that they had and told them, “I don’t know” for each of their questions. “But, remember, he is very frugal and he doesn’t want to spend a lot of money.” After that, I let them loose and many of the students’ work looked like this:

Student sample #1:

period 1 sample # 1

Student sample #2:

period 1 sample #2

Student sample #3:

period 1 sample #3

(This student’s comment made me LOL, but also cry at the same time when I saw the work in the top left corner…)

Overall, I felt great. The students were having great conversations, many were able to get the correct answer, and we did an extension question, where I asked students to figure out how the answer would change if there were 10 hot dogs in one package and 6 hot dog buns in one package. I went into the next class period feeling like I had a better game plan.

Second attempt

I decided to make the following changes:

  • Continue to provide background information about the movie
  • Don’t ask students, “What questions do you have?” or “What do you think we are trying to figure out?”
  • After showing the video clip, start the conversation with “Why is George so upset?”, followed by, “What would happen if he buys only one package of hot dogs and one package of hot dog buns?”
  • Ask students to complete sections about what information they knew and what information they need to solve the problem
  • Let students solve the question

The class started MUCH better and I was pretty proud of myself for making the changes above. The class list of information they knew and information they needed to solve the problem was similar to the first lesson attempt and I kept my response the same — “I don’t know.”

I walked around the classroom and one student asked me, “Mr. Luevanos, can there be more than one answer?” What in the world? I stopped myself from saying no and asked, “Tell me more about that.” The student began to explains that it depends on how many people are coming to dinner. I noticed he wasn’t alone and saw this among some students:

Student sample #4:

period 3 sample #4

Student sample #5:

period 3 sample #3

Student sample #6:

period 3 sample #2a

Are you thinking what I’m thinking?! O…M…G!

In this very moment, I couldn’t help but think of the great tune from “Van Halen II”…

You better call up the ambulance, I’m deep in shock.
Overloaded, baby, I can hardly walk.
Somebody get me a doctor!

These kids are finding not just one, but several common multiples for 8 and 12! Once I saw the students’ work and asked clarifying questions, I realized in that moment just how powerful this lesson is! I didn’t even consider that there are multiple answers to this question, but I saw this as a powerful teachable moment.

It took every ounce of my being to hold in my excitement and, somehow, I managed to stay calm. I had these three students share their strategies with the rest of the class and asked the following questions:

What do the numbers 8 and 12 represent?
Why are you adding 8 here? Why are you adding 12 here?
What does the number 24 represent?
How many packages of hot dogs and packages of hot dog buns will he need for 24 hot dogs?
Where do you see the number of packages of hot dogs and number of packages of hot dog buns in (student’s name)’s work?

Then, I dropped the bomb…and probably one of my most memorable moments in teaching. I asked:

Knowing that there is more than one correct answer and what you know about George Banks, which answer seems the most reasonable?”

Many students said 3 packages of hot dogs and 2 packages of hot dog buns, while some were unsure.

“Why?” I asked.

“Well, it depends on how many people are eating for dinner.”

“I think he’ll only want to buy enough food for 24 hot dogs because he doesn’t like to spend money.”

“Yeah! He’s cheap!”

“Oh yeahhhh!”

Hmm. Interesting. You are all correct. We don’t have enough information to decide whether he needs to buy enough food for 24, 48, 96 or more hot dogs. But…based on the information that we know, and knowing that George is careful with his money, which of the scenarios do you think George prefers such that he doesn’t have any extra hot dogs or hot dog buns?”

The class agreed that he would prefer to only buy 3 packages of hot dogs and 2 packages of hot dog buns. Here are some samples of student work:

Student sample #6 (continued):

period 3 sample #2b

Student sample #7:

period 3 sample #1

To wrap up the class, I told them, “Wow, this is so cool. And if I were George Banks, I would also prefer to not waste food and spend the least amount of money possible. What you just figured out is a topic you and your teacher will discuss in more detail tomorrow, which is known as the least common multiple.

Yes, I pretended that the Expo marker was a microphone and did a “mic drop” right before the bell rang. I was over the moon! One of my favorite days in teaching to date!

This made me more pumped for the next period. Now that I knew how great this lesson was, I made a few adjustments for the third class.

Third attempt

Here was my game plan for the third class:

  • Continue to provide background information about the movie
  • Start with the questions, with “Why is George so upset?”, followed by, “What would happen if he buys only one package of hot dogs and one package of hot dog buns?”
  • Ask students, “Okay, well let’s investigate how many packages of hot dogs and how many packages of hot dog buns he could buy?”
  • Ask students to complete sections about what information they knew and what information they need to solve the problem
  • Let students solve the question
  • Follow-up question, “Knowing what you know about George Banks, how many packages of hot dogs and how many packages of hot dog buns should he buy?”
  • Close the lesson linking to least common multiple

The class went phenomenal and better than I could imagine. Just by changing the question from should to could in the beginning really made a difference. The question made students think of as many scenarios as possible. I had more of an appreciation for the saying, “Third time’s a charm.” Here are some student work samples:

Student sample #8:

period 5 sample #1

Student sample #9:

period 5 sample #2

(The work on the bottom relates to the same extension question we did in first period)

Student sample #10:

period 5 sample #3

Student sample #11:

period 5 sample #4

(I think this student takes the cake…)

My Take-Aways

  1. I would highly encourage teachers to use this lesson as an introduction to least common multiple (check out Robert’s recent post about determining why we choose math problems in our classroom…great read). Many students came up with their own strategies that the teacher was planning on referring to with her formal lesson the next day.
  2. I would adjust the question in the beginning to, “How many packages of hot dogs and how many packages of hot dog buns could he buy?” Then, ask, “How many packages of hot dogs and how many packages of hot dog buns should he buy?”
  3. I would make sure that the teacher spends time at the end of the activity to formalize that this is known as the least common multiple for the students only if students have had the opportunity to have the conversation about which scenario George Banks would prefer and why.

I hope you see the beauty in this lesson. I had a blast teaching it and it was a great lesson for the beginning of the school year. Again, I cannot emphasize this enough…you
have to check out Robert’s website, try one of his lessons and subscribe to his blog. I promise you…you will benefit from his work and ideas. I sure have.

For those about to rock, we salute you!  
\m/  \m/


van halen

Absolutely! I mean…who doesn’t?!  I was a little kid when my uncle brought a vinyl of the Van Halen album to my parents’ house. He threw it on the record player and said, “Hey Danny, check this out.”

A crackle sound came through my parents’ old wooden speakers as the needle from the turntable hit the vinyl record. Is that the sound of a car horn or a train passing by? What are we listening to? As I’m trying to wrap my mind around what’s going on, the bass line drops, followed by tapping of the cymbals on the drum kit matching the beat. Then, I hear the great Eddie Van Halen lay down a powerful guitar riff! And to top it off, David Lee Roth comes into the mix hitting these crazy high vocal notes! In that moment, Van Halen gained a new fan — this guy.

This entire album is insane! It remains to be one of my favorite rock albums of all time. The guitar solos will literally melt your face and the harmonies add another dimension of greatness to each song. If you don’t believe, listen to this album the next time you drive to work and turn up the volume. You’ll be destined to have an amazing day. You can thank me later…I’ve lost count of how many times my brothers, uncles and I have rocked out to this record, pretending we are the members of Van Halen, air guitaring and singing our hearts out. Not going to lie…we’re pretty good.

But seriously, there’s no denying that Eddie Van Halen is incredibly talented. The man is flawless — a true musician and a master of his craft. He does the unthinkable by bringing sounds out of a guitar that seem impossible. He is a pivotal music icon whose style and sound changed rock music forever. I mean, have you listened to “Eruption”?! That song is transcendent — it’s loud, fast, and clean. To sum it up in one word, I’d say it’s unbelievable. I’ve never heard anything like it. I’ve listened to the song hundreds of times and, to me, it’s pure perfection. But, Eddie Van Halen has said before that, “I didn’t even play it right. There’s a mistake at the top end of it. To this day, whenever I hear it, I always think, ‘Man, I could’ve played it better.’”

Talk about a true legend. Only the greatest of the greats are ones who want to get better. There is no wonder why “Rolling Stone” magazine ranked him at #8 in the list of 100 greatest guitarists of all time in 2011. “Guitar World” magazine would disagree though…readers polled him at as #1 in 2012.

There’s one person in the math world who reminds me of Eddie Van Halen — Mr. Robert Kaplinsky.

I’m just going to come out and say it — Robert Kaplinsky is the man. The first time I saw his website reminded me of the first time I heard “Van Halen.” I was hooked immediately. Is that a picture of a huge pile of money? How much money is that?!…Wait, is that really a 100 x 100 In-N-Out burger?!…Not one, but TWO lessons relating to Dr. Evil?!…Man, I think this guy and I could be good friends. I then spent hours looking through his different lessons. They are all current, engaging and relevant. He provides detailed suggestions on how to structure each lesson, thoughtful questions to keep the student learning focused, anticipated student responses, extensions for breadth and depth, and sometimes his personal experience with the lesson. He thinks of everything.

Robert is constantly coming up with and sharing new ideas — ones that are fresh, exciting, necessary and inspiring. I’ve been fortunate to have had opportunities to work with Robert and seen him conduct professional development with teachers. He’s like watching Eddie Van Halen perform “Eruption” live (yes, I’ve seen Van Halen twice in concert and it was awesome). Robert is engaging, polished and extremely motivating. From start to finish, everyone is listening to what he has to say. He has an amazing gift at relating his classroom struggles with other teachers and identifying why we need to rethink our teaching practices and do something about it. He has so many one liners that make you stop and think, “Man, that is spot on!” He reminds me of John Wooden with all of his quotes that have resonated with me…

“The group is always smarter than the smartest person in the group.”
“What’s the least helpful question I can ask you?”
“It shouldn’t be the teacher’s job to create rigorous tasks. It should be the teacher’s job to be really good at implementing them.”
“Math education is complex, not complicated.”

The guy is legendary. I cannot begin to quantify how much Robert has taught me over the past two years. He has inspired me (and many others) to become better math educators. He has pushed me to challenge myself to step outside my comfort zone. He makes things look easy, which is a testament to his work ethic. He works incredibly hard, helps other educators get better and strives to deliver the best he can every single time. He takes major pride in his work and, like Eddie, is truly a master of his craft. The math education world has been waiting for pioneers like Robert to bring excitement back to learning mathematics and he is doing that everyday by encouraging all of us to productively struggle. I’m incredibly thankful for all that he has done for me and I’m honored to consider him my friend.

I can go on. I think it’s only appropriate for me to show you the amount of respect I have for the guy and I know many other math educators hold Robert in the same regard.

In my next post, I’ll share my awesome experience trying out one of Robert’s lesson for the first time.

Thank you, Robert, for all that you do. You continue to inspire me and I appreciate you coaching me along the way. You, my friend, are a math rockstar. You are the Eddie Van Halen in math education!

And, for the record (yes, pun intended), I listened to the album “Van Halen” on repeat while I was writing this blog post…on vinyl…on my parents’ record player which they gave me a few years ago…

There’s nothing like the cracking sound of the vinyl…

For those about to rock, I salute you!  
\m/  \m/


Imagine this…It’s 5 AM. Friday morning. Driving on the freeway. Darkness. Headlights are passing by. “Why are people awake at this hour?” You’re trying to drink your cup of coffee and wake up but you can’t fight back the yawns. The sun slowly starts to come over the horizon. Your eyes begin to squint. All of a sudden, something amazing happens…Your head starts moving back and forth without you knowing. Your ears hear one of the most iconic opening guitar riffs of all time playing on your stereo…and then…

Welcome to the jungle
We’ve got fun ‘n’ games
We got everything you want
Honey, we know the names
We are the people that can find
Whatever you may need
If you got the money, honey
We got your disease

Talk about an adrenaline rush! The timing of this song couldn’t be more perfect as I was driving to Palm Springs for CMC-S two weeks ago. Yes, this song was on repeat in my mind throughout the rest of the conference, and I couldn’t help but realize that the lyrics of the song sum up my experience. CMC-S 2015 was just like this great Guns ‘N Roses song — epic.

Where do I begin?


If you ever have the opportunity to go to a math conference, you HAVE to see the following people present — and that’s non-negotiable.

Some of these speakers I met for the first time at CMC-S 2015, and others I have the privilege of calling my friends. Each and every one of them are great, friendly people who will make you want to be a better math educator. Please note that this is not my exhaustive list. There are many others who I didn’t have the opportunity to see or meet. Two days isn’t enough…


  1. #MTBoS was definitely the cat’s pajamas all weekend long. It was the buzz in every session I went to and every conversation I had during the two-day conference. What was fascinating is every person — at some point — mentioned that the Math Twitter Blogosphere community has helped them grow more than anything else in their teaching career. The message was and has always been clear… “We are stronger and better together!” Not only that, everyone in the MTBoS community believes in this statement! I cannot articulate into words what it was to hear that message consistently. It’s something so powerful that cannot be replicated by reading the words in a blog or a tweet — you really have to experience it. All I can say is…wow. I believe now more than ever that the sky is truly the limit and #MTBoS is the driving force. 
  2. Every session put a great emphasis on the 8 Standards of Mathematical Practice and how they need to be at the forefront of everything we do as math teachers for all of our students. I couldn’t agree more. In the words of Cosmo Kramer, I like to think of the 8 SMPs as the “straw that stirs the drink.” It’s what makes learning mathematics a beautiful work of art. They are the heart and soul of the mathematics classroom and the skills we want our students to take with them into the real world when they leave our classroom. We need to continue to get the word out! 
  3. The Ignite Session was unreal and I will make sure not to miss one at future Math Conferences. What a great segment in the conference and an entertaining experience! There were lots of laughs and a few tears shed, all of which made you want to go out and change the world. It’s now a goal of mine to have an opportunity to be one of Ignite speakers. And great job of emceeing, Mr. Brian Shay. You definitely made the night more fun!


To all who presented, those I met, and those I got to hang out with at CMC-S…

Thank you for inspiring me. Thank you for pushing me to ask myself the question, “What’s next?” Thank you for make me see the hidden gems in our students’ mistakes. Thank you for teaching me that a mathematical argument is more than just volume — it takes eloquence, style, and tone. Thank you for reminding me that it’s not our job as math teachers to simply create content, but to implement the content well. Thank you for encouraging me to do more lesson planning, not lesson pacing. Thank you for helping me realize all students have the right to productively struggle. Thank you for your honesty. Thank you for sharing your story. Thank you for helping me believe in myself and that I have something valuable to contribute.

Meow…just like the song, when people ask me, “How was your time at CMC-S?,” here’s what I would tell them…

Fun is an understatement.
I got more than I wanted and needed out of the conference
I met incredible people along the way.
I left inspired, wanting more, and wondering more.
I know CMC-S will not disappoint in the future.
I will be back.

In the words of the greatest rock band of all time, AC/DC…“For those about to rock, I salute you.”

\m/  \m/